Estimating a transmission channel with pilot symbols distributed in lattice structure

ABSTRACT

A method for estimating a transmission channel from a multicarrier signal transmitted through said transmission channel, comprising real pilot symbols and so-called pure imaginary pilot symbols, consists in selecting one or several values z k  of the received signal corresponding respectively to one or several real pilot symbols, and one or several values z l  of the received signal corresponding respectively to one or several pure imaginary pilot symbols. The pilot symbols are sufficiently close both in frequency and in time such that it can be assumed that the fading of the signal through the transmission channel has a complex value α substantially identical for the symbols. An estimated value {circumflex over (α)} of α for the pilot symbols concerned is then determined by minimizing a least square equation involving the values z k  and the values z l .

TECHNICAL FIELD

The present invention relates to a method of estimating a transmissionchannel, and to devices for the implementation of the method.

It concerns the field of digital transmissions by radiofrequency carrierwaves (digital radio transmissions). It finds applications in particularin receivers of systems for digital radiocommunications with mobiles,for example professional radio-communications systems (PMR systems, theabbreviation standing for “Professional Mobile Radio”).

BACKGROUND OF THE INVENTION

In these systems, the digital data are transmitted by modulation of aradiofrequency carrier wave. Stated otherwise, a radio signal is sentover the transmission channel, this signal being modulated so as tocarry the digital information to be transmitted.

The expression “estimating the transmission channel” is understood tomean in a conventional manner estimating the conditions of propagationof the radio signal through the latter, which affect the signaltransmitted.

One seeks to implement modulation techniques that offer betterresistance with regard to disturbances undergone by the radio signalduring its transmission through the transmission channel. In essence,these disturbances originate:

-   -   on the one hand from the fading phenomenon, which is frequency        selective as soon as the coherence band is overstepped (one        speaks in this first case of selective fading), but which is not        frequency selective once the width of the channel is less than        the coherence band (one speaks in this latter case of flat        fading). This fading phenomenon is due to the propagation        multipaths which give rise to intersymbol interference (ISI)        also known as intersymbol distortion;    -   on the other hand, from the fact that the amplitude and the        phase of the or of each of the propagation paths may be static        (in the sense that they do not vary in the course of time) or on        the contrary dynamic (when the propagation conditions vary in        the course of time). In the dynamic case, the frequency of this        phenomenon (also called the frequency of the fading) and, more        generally, the frequency spectrum of the fading are related to        the speed of the mobile and to the carrier frequency of the        signal sent. The conventional model adopted for the power        spectrum of the fading is described in the work “Microwave        Mobile Communications”, by William C. Jakes, Jr., published by        John Wiley & Sons, 1974, pp. 19-25), and involves the Doppler        frequency f_(D) given by:

$\begin{matrix}{f_{D} = {\frac{V}{c} \times f_{c}}} & (1)\end{matrix}$

where V is the speed of the mobile, c is the speed of light, and f_(c)is the frequency of the radiofrequency carrier.

There is currently effort to seek to implement a multicarrier modulationcalled OFDM (standing for “Orthogonal Frequency Division Multiplexing”).This modulation technique has been adopted for the European standardregarding digital audio broadcasting systems (DAB systems, theabbreviation standing for “Digital Audio Broadcasting”). It consists indistributing the data to be transmitted over a set of subcarriers sentin parallel in the radio signal. This results in a flat fading effect inrelation to each subcarrier since the bandwidth of each subcarrier isless than the coherence band. Furthermore, it results in a reduction inthe sensitivity of transmission in relation to the phenomenon ofmultipaths.

The signal to be transmitted is constructed on a time/frequency lattice.Such a time/frequency lattice comprises a set of symbols, constituting atwo-dimensional space which is defined by a frequency axis and by a timeaxis. It is recalled that a symbol corresponds to a determined number ofinformation bits, for example 8 bits, which takes a determined value inan ad-hoc alphabet. By convention, the frequency axis is representedvertically and the time axis is represented horizontally. Each symbol istagged by an index m along the frequency axis, and by an index n alongthe time axis. By convention, a symbol whose position along thefrequency axis is defined by the index m, and whose position along thetime axis is defined by the index n is in general denoted S_(m,n).Finally, the spacing between the symbols along the frequency axis isdenoted γ₀. Likewise, the spacing between the symbols along the timeaxis is denoted τ₀.

If S(t) denotes a signal constructed on such a lattice of symbols, thesignal S(t) can be decomposed into the form:

$\begin{matrix}{{S(t)} = {\sum\limits_{m,n}{c_{m,n} \times {\mathbb{e}}^{2 \cdot {\mathbb{i}} \cdot m \cdot \gamma_{0}} \times {g( {t - {n \cdot \tau_{0}}} )}}}} & (2)\end{matrix}$

where the sign Σ designates the summation operation;

where the coefficients c_(m,n) are coefficients corresponding to thevalue of the symbol S_(m,n); and

where the function g(t) designates the shaping pulse for the modulation.

The signal to be transmitted is structured as frames that aretransmitted in succession through the transmission channel. Each framecomprises a number M of adjacent subcarriers inside a channel ofdetermined spectral width, each of these subcarriers being divided intoN time intervals, called symbol times, which are transmitted insuccession through the transmission channel. The duration of a symboltime corresponds to the duration of transmission of a symbol. A frame ofthe signal therefore comprises M×N symbols. The aforesaid parameter γ₀represents the spacing between two adjacent subcarriers, and theaforesaid parameter τ₀ represents the spacing between two successivesymbols on one and the same subcarrier.

In systems using OFDM type modulation, the shaping pulses for themodulation are chosen in such a way that each symbol is orthogonal withall the other symbols. The lattice is then said to be orthogonal. Bydefinition, symbols are mutually orthogonal if their scalar product iszero.

This characteristic makes it possible to simplify demodulation.

Systems using OFDM modulation subdivide into two categories.

On the one hand, the systems using a time/frequency lattice of density 1(subsequently referred to as “systems of density 1”, for short) forwhich the product γ₀×τ₀ is equal to unity (γ₀×τ₀=1). In these systemsthe modulated symbols may be complex symbols. The aforesaid coefficientsc_(m,n) are then complex numbers. We can writec_(m,n)=a_(m,n)+i×b_(m,n), where a_(m,n) and b_(m,n) are real numbers.This offers the possibility of employing both amplitude modulation andphase modulation. In practice, a guard must however be taken in thefrequency domain and/or in the time domain between two consecutiveadjacent symbols along the frequency axis, respectively along the timeaxis. This guard substantially reduces the maximum throughput (expressedas a number of symbols per second, or baud) which may flow through thetransmission channel.

On the other hand, systems using a time/frequency lattice of density 2(subsequently referred to as “systems of density 2”, for short) forwhich the product γ₀×τ₀ is equal to

$\frac{1}{2}{( {{\gamma_{0} \times \tau_{0}} = \frac{1}{2}} ).}$In these systems, the maximum throughput (expressed as a number ofsymbols per second, or baud) is twice as high as in the systems ofdensity 1. However, in systems of density 2, the modulated symbols mustbe one-dimensional, that is to say they either have a real value (onethen speaks of real symbols), or a pure imaginary value (one then speaksof pure imaginary symbols). We can write c_(m,n)=a_(m,n) for the realsymbols or c_(m,n)=i×b_(m,n) for the pure imaginary symbols, wherea_(m,n) and b_(m,n) are real numbers. More precisely, if a symbol isreal, its immediate neighbors, that is to say the symbols situated onthe same subcarrier in the immediately previous and immediatelysubsequent symbol times (with reference to the order of sending of thesymbols over the transmission channel, that is to say the symbols thatare adjacent in the direction of the time axis) and the symbols that aresituated in the same symbol time on the subcarriers placed on theimmediately higher and immediately lower frequencies (i.e., the symbolsthat are adjacent in the direction of the frequency axis), are pureimaginary. Conversely, if a symbol is pure imaginary, its immediateneighbors, that is to say the symbols adjacent in the direction of thefrequency axis and the symbols adjacent in the direction of the timeaxis, are real. Systems of density 2 do not require the presence of afrequency guard or time guard. They therefore make it possible totransport a higher throughput than systems of density 1.

In what follows, only the case of systems of density 2 will beconsidered. The invention applies in fact to systems of this type.

A particular example of an OFDM type modulation in a system of density 2is so-called OFDM/IOTA modulation (the initials standing for“OFDM/Isotropic Orthogonal Transform Algorithm”). The way in which atime/frequency lattice that is orthogonal with such a modulation can bedefined is described for example in the article “Coded OrthogonalFrequency Division Multiplex”, Bernard L E FLOCH et al., Proceedings ofthe IEEE, Vol. 83, No. 6, June 1995).

The coefficients c_(m,n) are then either real numbers or pure imaginarynumbers, depending on the placement of the symbol S_(m,n) in the frame.They are therefore always one-dimensional. This offers only thepossibility of amplitude modulation. Nevertheless, it is not necessaryto guarantee a guard time between the symbols or between thesubcarriers, this having the advantage of increasing the transmissionthroughput.

Therefore, half the symbols transmitted are real and half are pureimaginary. These symbols are shaped by the modulation pulse g(t)mentioned earlier. This pulse extends over the time axis, over aduration corresponding to several symbols, and/or over the frequencyaxis, over frequencies corresponding to several subcarriers.

On receipt of a radio signal, a time and frequency synchronization ofthe signal received is performed. The signal received is then correlatedwith the signal expected, that is to say a correlation of the signalreceived with the modulation pulse g(t) is performed. This correlationmay be performed by various procedures, for example by performing amultiplication by the modulation pulse g(t) then an FFT (standing for“Fast Fourier Transform”).

Thereafter it is appropriate to proceed with the estimation of thepropagation conditions over the transmission channel, that is to say theestimation of the transmission channel, also called estimation of fadingsince it produces an estimated value of the fading of the signaltransmitted through the transmission channel. Specifically, thesepropagation conditions have to be taken into account when demodulatingthe signal received, and more precisely when estimating the value of thesymbols transmitted.

SUMMARY OF THE INVENTION

The present invention proposes a channel estimating procedureappropriate for system of density 2, that is to say systems using OFDMmodulation based on a time/frequency lattice of density 2.

According to a first aspect of the invention, there is in fact proposeda method of estimating a transmission channel on the basis of a signalreceived after transmission through said transmission channel, saidsignal being a multicarrier signal constructed on a time/frequencylattice defined by a frequency axis and a time axis, and comprisingframes having M×N symbols distributed over M subcarriers each of whichis divided into N determined symbol times, each frame comprising P pilotsymbols distributed timewise and frequencywise in such a way as to coverthe frame according to a lattice structure, where the numbers M, N and Pare nonzero integers, the pilot symbols comprising on the one handsymbols known as real pilot symbols, transmitted as symbols having areal value, and on the other hand symbols known as pure imaginary pilotsymbols, transmitted as symbols having a pure imaginary value, themethod comprising the steps consisting in:

a) selecting one or more values z_(k) of the signal receivedcorresponding to one or more real pilot symbols of respective valuesc_(k) on the one hand, and one or more values z_(l) of the signalreceived corresponding respectively to one or more pure imaginary pilotsymbols of respective values c_(l) on the other hand, these pilotsymbols being sufficiently close together both along the frequency axisand along the time axis for it to be possible to consider that thefading of the signal through the transmission channel has had asubstantially identical (in modulus and in phase) complex value α forthese pilot symbols;

b) determining complex numbers u and v and a real number λ by minimizingthe following least squares expression:

$ɛ_{1}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot u} )} - {\lambda \cdot c_{k}}}}^{2}} + {\sum\limits_{1}{{{{Re}( {z_{1} \cdot v} )} - {\lambda \cdot c_{1}}}}^{2}}}$

where the sign Σ denotes the summation operator,

where ∥x∥ denotes the absolute value operator for the real variable x orthe modulus of the complex variable x,

where Re(w) denotes the real part operator for the complex number w,

where λ is a real number, and

where u and v are orthogonal (that is to say Re(u*.v)=0, where w*denotes the complex conjugate of the complex number w), such that∥u∥=∥v∥,

c) determining an estimated value & of the value a of the fading of thesignal through the transmission channel for the pilot symbols concerned,by calculating:{circumflex over (α)}=λ/u.

The invention therefore makes it possible to estimate values of thefading in a system of dimension 2. The steps of the method are repeatedby selecting other pairs or groups of pilot symbols, in such a way as toproduce sufficiently many estimated values of the fading to allowchannel tracking.

According to a second aspect of the invention, there is also proposed adevice comprising means for the implementation of this method.

The device comprises:

-   -   means for selecting one or more values z_(k) of the signal        received corresponding to one or more real pilot symbols of        respective values c_(k) on the one hand, and one or more values        z_(l) of the signal received corresponding respectively to one        or more pure imaginary pilot symbols of respective values c_(l)        on the other hand, these pilot symbols being sufficiently close        together both along the frequency axis and along the time axis        for it to be possible to consider that the fading of the signal        through the transmission channel has had a substantially        identical (in modulus and in phase) complex value α for these        pilot symbols;    -   means for determining complex numbers u and v and the real        number λ minimizing the following least squares expression:

$ɛ_{1}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot u} )} - {\lambda \cdot c_{k}}}}^{2}} + {\sum\limits_{1}{{{{Re}( {z_{1} \cdot v} )} - {\lambda \cdot c_{1}}}}^{2}}}$

where the sign Σ denotes the summation operator,

where ∥x∥ denotes the absolute value operator for the real variable x

where u and v are orthogonal (that is to say such that Re(u*.v)=0) suchthat ∥u∥=∥v∥, and

where λ is a real number,

-   -   and means for determining an estimated value {circumflex over        (α)} of the fading of the signal through the transmission        channel for the pilot symbols concerned, by calculating:        {circumflex over (α)}=λ/u.

According to a first mode of implementation of the method, λ is equal tounity, u is equal to β, and v is equal to −i˜β, where β denotes theinverse of α,

so that step b) consists in determining real numbers Re(β) and Im(β)which minimize the following least squares expression:

$ɛ_{2}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot \beta} )} - c_{k}}}^{2}} + {\sum\limits_{1}{{{{Im}( {z_{1} \cdot \beta} )} - c_{1}}}^{2}}}$

where the sign Σ denotes the summation operator,

where ∥x∥ denotes the absolute value operator for the real variable x

where Re(x) denotes the real part operator for the complex variable x,and

where Im(x) denotes the imaginary part operator for the complex variablex;

and so that step c) consists in determining the estimated value{circumflex over (α)} of the value α of the fading of the signal throughthe transmission channel for the pilot symbols concerned, by invertingthe complex number Re(β)+i·Im(β).

According to a third aspect of the invention, there is also proposed adevice for the implementation of the method in accordance with thisfirst mode of implementation.

The device comprises:

-   -   means for selecting one or more values z_(k) of the signal        received corresponding to one or more real pilot symbols of        respective values c_(k) on the one hand, and one or more values        z_(l) of the signal received corresponding respectively to one        or more pure imaginary pilot symbols of respective values c_(l)        on the other hand, these pilot symbols being sufficiently close        together both along the frequency axis and along the time axis        for it to be possible to consider that the fading of the signal        through the transmission channel has had a substantially        identical complex value α for these pilot symbols;    -   means for determining real numbers Re(β) and Im(β) minimizing        the following least squares expression:

$ɛ_{2}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot \beta} )} - c_{k}}}^{2}} + {\sum\limits_{1}{{{{Im}( {z_{1} \cdot \beta} )} - c_{1}}}^{2}}}$

where the sign Σ denotes the summation operator,

where ∥x∥ denotes the absolute value operator for the real variable x

where Re(x) denotes the real part operator for the complex variable x,

where Im(x) denotes the pure imaginary part operator for the complexvariable x, and

where β denotes the inverse of α; and,

means for determining an estimated value {circumflex over (α)} of thefading of the signal through the transmission channel for the pilotsymbols concerned, by inverting the complex number Re(β)+i·Im(β).

According to a second mode of implementation of the method, whichconstitutes a preferred mode, λ is equal to ρ, u is equal to e^(−i·φ),and v is equal to −i·e^(−i·φ), where ρ and φ are real numbers thatrespectively denote the modulus and the phase of {circumflex over (α)}({circumflex over (α)}=ρ·e^(i·φ)),

so that step b) and step c) are carried out jointly and consist indetermining an estimated value {circumflex over (α)} of the fading ofthe signal through the transmission channel for the pilot symbolsconcerned, which value is defined by {circumflex over (α)}=ρ·e^(i·φ)where ρ and φ minimize the following least squares expression:

$ɛ_{3}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{k}}}}^{2}} + {\sum\limits_{1}{{{{Im}( {z_{1} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{1}}}}^{2}}}$

where the sign Σ denotes the summation operator,

where ∥x∥ denotes the absolute value operator for the real variable x

where Re(x) denotes the real part operator for the complex variable x,and

where Im(x) denotes the pure imaginary part operator for the complexvariable x.

This mode of implementation is preferred since it makes it possible toobtain the value of α directly, in the sense that it comprises no finalstep of inverting a complex number. It is therefore faster.

According to a fourth aspect of the invention, there is finally proposeda device for the implementation of the method in accordance with thissecond mode of implementation.

The device comprises:

-   -   means for selecting one or more values z_(k) of the signal        received corresponding to one or more real pilot symbols of        respective values c_(k) on the one hand, and one or more values        z_(l) of the signal received corresponding respectively to one        or more pure imaginary pilot symbols of respective values c_(l)        on the other hand, these pilot symbols being sufficiently close        together both along the frequency axis and along the time axis        for it to be possible to consider that the fading of the signal        through the transmission channel has had a substantially        identical complex value α for these pilot symbols; and,    -   means for determining an estimated value {circumflex over (α)}        of the fading of the signal through the transmission channel for        the pilot symbols concerned, which value is defined by        {circumflex over (α)}=ρ·e^(i·φ) where ρ and φ are real numbers        which minimize the following least squares expression:

$ɛ_{3}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{k}}}}^{2}} + {\sum\limits_{1}{{{{Im}( {z_{1} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{1}}}}^{2}}}$

where the sign Σ denotes the summation operator,

where ∥x∥ denotes the absolute value operator for the real variable x

where Re(x) denotes the real part operator for the complex variable x,and

where Im(x) denotes the pure imaginary part operator for the complexvariable x.

BRIEF DESCRIPTION OF THE DRAWINGS

in FIG. 1: a chart illustrating a time/frequency lattice on which thesignal transmitted over the transmission channel is constructed;

in FIG. 2: a chart illustrating the structure of a frame of amulticarrier signal according to an exemplary embodiment of theinvention;

in FIG. 3: a chart illustrating the steps of a method of demodulating aradio signal received by a receiver after transmission through atransmission channel;

in FIGS. 4 a to 4 c: charts of steps illustrating the method accordingto the invention respectively in the general case, according to a firstmode of implementation and according to a second mode of implementation;

in FIG. 5: a schematic diagram illustrating devices according to theinvention.

DESCRIPTION OF PREFERRED EMBODIMENTS

The chart of FIG. 1 illustrates a time/frequency lattice of a system ofdensity 2, such as for example a system using OFDM/IOTA modulation.

The lattice is defined by a frequency axis (here, the vertical axis) andby a time axis (here, the horizontal axis). The lattice comprises a setof symbols represented symbolically here by small horizontal or verticalarrows. The spacing between the symbols along the frequency axis isdenoted γ₀. Likewise, the spacing between the symbols along the timeaxis is denoted τ₀. According to intrinsic properties of thetime/frequency lattice, each symbol is orthogonal with all the othersymbols.

In FIG. 1, the symbols represented by horizontal arrows are realsymbols. Those represented by vertical arrows are pure imaginarysymbols. As stated in the introduction, if a determined symbol is real,its immediate neighbors, that is to say the symbols situated directly toits right or to its left in the direction of the time axis and thesymbols situated directly above or below it in the direction of thefrequency axis, are pure imaginary. Conversely, if a determined symbolis pure imaginary, its immediate neighbors (defined in the same manneras above) are real. For example the symbol situated at the intersectionof the time axis and the frequency axis (called the useful symbol) is areal symbol.

A multicarrier signal may be constructed on such a time/frequencylattice, by being structured as successive frames transmitted over thetransmission channel. A frame is defined along the frequency axis andalong the time axis, respectively by a frequency band B, and by aduration D. It comprises M subcarriers, where M is an integer such thatB=M×γ₀. Moreover, each subcarrier is divided into N symbol times, whereN is an integer such that D=N×τ₀. The frame therefore comprises M×Nsymbols.

The chart of FIG. 2 represents the structure of a frame of a multicarrersignal according to an example appropriate for the implementation of theinvention.

By convention, a double order relation is defined for tagging thelocation of a symbol in the frame along the frequency axis on the onehand, and along the time axis on the other hand. According to this orderrelation, the symbol S_(1,1) is the symbol which is carried on the firstsubcarrier (that corresponding to the index m equal to unity (m=1)) andwhich is transmitted first on this subcarrier, that is to say which issituated in the first symbol time (that corresponding to the index nequal to unity (n=1)). This symbol S_(1,1) is represented at the bottomleft in the figure. Likewise, the symbol S_(M,N) is the symbol which iscarried on the last subcarrier of the frame (that corresponding to theindex m equal to M (m=M)) and which is transmitted last on thissubcarrier, that is to say which is situated in the last symbol time(that corresponding to the index n equal to N (n=N)). This symbolS_(M,N) is represented at the top right in the figure. Generally, thesymbol S_(m,n) is the symbol which is carried on the m-th subcarrier ofthe frame (that of index m) and which is transmitted on this subcarrierin the n-th symbol time (that of index n).

In order to allow channel tracking, the frame contains P pilot symbols,where P is an integer in principle much less than M×N. It is recalledthat a pilot symbol is a symbol whose location in the frame and whosevalue are known to the receiver. The pilot symbols are distributedtimewise and frequencywise, in such a way as to cover the frameaccording to a lattice structure.

In the example represented, the signal occupies a frequency band B=44kHz (kilohertz) within a radio channel 50 kHz wide. Moreover the spacingbetween the subcarriers is γ₀=2 kHz. The frame therefore comprises M=22subcarriers.

Moreover the duration of the frame is D=20 ms (milliseconds). Thethroughput over each subcarrier is 4 kilosymbols/s (thousands of symbolsper second), hence the temporal spacing between the symbols is τ₀=250μs. Stated otherwise, the frame comprises N=80 symbol times.

The frame therefore comprises M×N=1760 symbols. In the figure, the pilotsymbols are represented by gray cells, and the other symbols, whichcorrespond to useful information, are represented by white cells. Out ofthe 1760 symbols of the frame, there are 206 symbols that are pilotsymbols. Stated otherwise, P=206.

Certain of the pilot symbols, which are pairwise adjacent in thedirection of the frequency axis and/or in the direction of the timeaxis, form a block of pilot symbols such as 51 or 53. In the example,the frame indeed comprises blocks of pilot symbols. A block of pilotsymbols is defined in the sense that it is a group of pilot symbols,that may or may not be adjacent in the direction of the frequency axisand/or in the direction of the time axis, and for which a doublecondition of stationarity in time and stationarity in frequency of thetransmission channel is satisfied.

By convention, in what follows, the position of a block of pilot symbolsin the frame is tagged by the position of the pilot symbols of thisblock which is on the carrier of smallest index, and in the symbol timetransmitted first (in the figures, this is, for each block, the pilotsymbol which is the lowest and the leftmost). Likewise, the size of theblock is defined by a dimension along the frequency axis (hereinafter“height”, denoted h) expressed as a number of symbols, and by adimension along the time axis (hereinafter “length”, denoted l),expressed as a number of symbols. The size of the block is denoted h×l,where h designates the height and l designates the length of the block.

This convention is convenient in cases where the blocks of pilot symbolshave regular dimensions (forming not examples of rows, or of patches ofpilot symbols, that is to say squares or rectangles), as is the case inthe example represented. Nevertheless, it is understood that a block ofpilot symbols may have an irregular structure (for example three pilotsymbols that are pairwise adjacent but not aligned).

Furthermore, it is specified that the concept of block of pilot symbolsaccording to the invention does not necessarily correspond to a conceptof adjacency but rather to a concept of proximity both in the directionof the frequency axis and in the direction of the time axis. In reality,the definition of a block of pilot symbols is as follows: the pilotsymbols of one and the same block, which may or may not be adjacent, areconsidered to be symbols satisfying a double condition of frequencystationarity and of time stationarity of the conditions of propagationover the transmission channel.

These two conditions may be translated into terms of maximum spacing ofthe pilot symbols, respectively in the direction of the frequency axisand in the direction of the time axis, as will be made explicit in thenext paragraph. As a result, the maximum dimensions of a block of pilotsymbols according to the invention depend on the propagationcharacteristics, the latter therefore having to be taken into account bythe system designer when choosing the distribution of the pilot symbolsin the frame.

It is known that the characteristics of the propagation through thetransmission channel are defined by the maximum frequency of thevariations in fading (called the “fading frequency” in the jargon of theperson skilled in the art) and the maximum delay between the multipaths.In an example, for propagation of HT (“Hilly Terrain”) type which is themost constraining, it has been established that the fading frequency isequal to 148.2 Hz (hertz) for a maximum speed of travel of the mobileequal to 200 km/h (kilometers per hour) and for a carrier frequencyequal to 400 MHz (megahertz), on the one hand, and that the maximumdelay between the multipaths corresponds to ±7.5 μs (microsecond), i.e.a maximum delay between the most advanced path and the most delayed pathof 15 μs, on the other hand.

Now, for a throughput of 4 kilosymbols/s per subcarrier, the frame mustcomprise pilot symbols (or blocks of pilots) with a spacing in thedirection of the time axis, called the temporal spacing, which must beless than the inverse of the fading frequency, that is to say it mustcomprise a pilot symbol every 27 symbols at most.

This maximum spacing of 27 symbols along the direction of the time axiscorresponds to a sampling of the propagation channel (fading) performedfaster (even only slightly faster) than the occurrence of the successivefadeouts (zero crossing of the fading on the time axis). Between twosuccessive fadeouts, the phase of the fading has rotated by π (numberPI). Over, for example, a tenth of this period between fadeouts, that isto say over a period corresponding to 2.7 successive symbols, the fadingwill have rotated by π/10. In what follows, a group having twosuccessive symbols along the time axis will be considered for practicalreasons. Between these two successive symbols, the fading will haverotated by π/27. If the fading in the middle of this period of twosymbols has a certain determined value F_(m), the fading at the end ofthis period of two symbols will have a value F_(f) which will be veryclose to F_(m)×e^(i·π/54). Hence, we have a quadratic error given by:ε_(f) ² =F _(m) −F _(f)∥² =∥F _(m)∥²×(2×sin(π/(2×54)))² =∥F_(m)∥²×0.00338  (3)

i.e. a signal-to-noise ratio of: 24.71 dB.

Likewise if the fading at the start of this period of two symbols has acertain determined value F_(d), then in the middle of this period wehave a quadratic error given by:ε_(d) ² =∥F _(m) −F _(d)∥² =∥F _(m)∥²×(2×sin(π/(2×54)))² =∥F_(m)∥²×0.00338  (4)

i.e. the same signal-to-noise ratio of: 24.71 dB.

Hence, there is no disadvantage in considering the channel to bestationary timewise over a duration corresponding to two successivesymbol times, that is to say two adjacent symbols in the direction ofthe time axis.

Likewise, for propagation of HT type, which exhibits a maximum delaybetween paths of 15 μs, and for a spacing between subcarriers of 2 kHz,the frame must comprise pilot symbols with a spacing along the frequencyaxis, called the frequency spacing, which must be less than the inverseof the maximum delay between the multipaths, i.e. one pilot symbol every33 subcarriers at most.

This spacing of 33 subcarriers along the direction of the frequency axiscorresponds to a frequency sampling of the channel more frequently (evenonly slightly more frequently) than the occurrence of the successiveholes in frequency selectivity (zero crossing of the level of the signalreceived at certain frequencies). Between two successive holes infrequency selectivity the phase of the fading has rotated by π. Over,for example, a tenth of this space between frequency selectivity holes,that is to say over a frequency band corresponding to 3.3 subcarriers,the fading will have rotated by π/10. A band corresponding to 3subcarriers will be considered for practical reasons. Between theextreme subcarriers of this band, the fading will have rotated by(π/33)×2. If the fading in the middle of the frequency band comprisingthese three subcarriers has a certain determined value F_(m), the fadingfor the highest frequency subcarrier of this group of three subcarrierswill have a value F_(f) which will be very close to F_(m)×e^(i·π/33)).

Hence, there is a quadratic error given by:ε_(f) ² =∥F _(m) −F _(f)∥² =∥F _(m)∥²×(2×sin(π/(2×33)))² =∥F_(m)∥²×0.00906  (5)

i.e. a signal-to-noise ratio of 20.43 dB.

Likewise if the fading for the lowest frequency subcarrier of this groupof three subcarriers has a determined value F_(d), then in the middle ofthis period there is a quadratic error given by:ε_(d) ² =∥F _(m) −F _(d)∥² =∥F _(m)∥²×(2×sin(π/(2×33)))² =∥F_(m)∥²×0.00906  (6)

i.e. the same signal-to-noise ratio of 20.43 dB.

Hence, without any disadvantage, the channel may be regarded asfrequencywise stationary over a frequency band corresponding to threeadjacent subcarriers, that is to say to three adjacent symbols in thedirection of the frequency axis.

As a consequence of the foregoing, pilot symbols which are not spacedmore than two symbols apart along the time axis or more than threesymbols apart along the frequency axis may be regarded as satisfying adouble condition of time and frequency stationarity, of the conditionsof propagation over the transmission channel (i.e. of the fading).

It will be noted that the considerations regarding the stationarity ofthe fading set forth hereinabove are to be assessed as a function of theproblem to be treated, that is to say in particular of thecharacteristics of the envisaged propagation, of the speed of themobile, and of the carrier frequency.

In the general case, this amounts to saying that, as soon as the pilotsymbols are sufficiently close together both along the frequency axisand along the time axis, the fading of the signal through thetransmission channel may be considered to have a substantially identicalcomplex value for these pilot symbols.

In conclusion, it is thus possible to give the definition of a block ofpilot symbols within the sense of the present invention: a block ofpilot symbols according to the invention is defined in the sense that itis a group of pilot symbols, that may or may not be adjacent in thedirection of the time axis and/or in the direction of the frequencyaxis, and for which a double condition of time stationarity and offrequency stationarity of the propagation conditions of the transmissionchannel is satisfied. It will then be possible to make the assumptionthat the symbols of such a block have been affected by fading having anidentical value (in modulus and in phase).

In the example represented in FIG. 2, the frame comprises at least oneblock of six pilot symbols of dimensions 3×2, that is to say dimensionsalong the frequency axis and along the time axis correspond respectivelyto three symbols (h=3) and to two symbols (l=2).

According to the example, the frame comprises more exactly 32 blockssuch as 51, of six pilot symbols each, whose dimensions along thefrequency axis and along the time axis correspond respectively to threesymbols and to two symbols. Their respective locations in the frame,which are tagged by the location of the pilot symbol of the blockconsidered which is in the subcarrier of lowest frequency and in thesymbol time transmitted first (i.e., the bottommost and leftmostsymbol), are the locations of the symbols S_(m,n) (it is recalled that mand n are integer indices which tag the position of the symbol along thefrequency axis and along the time axis respectively), with m lying inthe set {1, 7, 14, 20} and with n=1+11xj, where j is an integer lying inthe set [0;7].

Furthermore, the frame comprises a first supplementary block 52 of sixpilot symbols whose dimensions along the frequency axis and along thetime axis correspond respectively to three symbols and to two symbols.

It also comprises a second supplementary block 53 of eight pilot symbolswhose dimensions along the frequency axis and along the time axiscorrespond respectively to four symbols and to two symbols.

The respective locations of the supplementary block 52 and of thesupplementary block 53 in the frame, which are tagged by the location ofthe pilot symbol of the block considered which is in the subcarrier oflowest frequency and in the symbol time transmitted first (i.e., thebottommost and leftmost symbol), are the locations of the symbolsS_(m,n) with the pair (m,n) lying in the set of pairs {(4,1), (10,1)}.Stated otherwise, the blocks 52 and 53 are positioned on the symbolsS_(4,1) and S_(10,1) respectively.

The supplementary blocks of pilot symbols 52 and 53, in combination withthe blocks 51 which are adjacent to them, are used by the receiver forframe synchronization.

Represented in FIG. 3 are the main steps of a demodulation methodimplemented by a receiver of a digital radiocommunications system.

In a step 31, the receiver performs a time and frequency synchronizationof its processing circuits with the frame structure of the signalreceived. This synchronization is performed by means of the blocks ofsupplementary pilot symbols 52 and 53 in combination with the blocks ofpilot symbols 51 which are adjacent to them in the direction of thefrequency axis, as indicated above. The detailed description of thisstep would depart from the scope of the present account.

In a step 32, and for each symbol transmitted, denoted S_(p) in whatfollows (where the index p corresponds to a pair of indices m,n fortagging the position of the symbol in the frame), this signal receivedis correlated with the expected signal, that is to say a correlation ofthe signal received with the modulation pulse g(t) is performed. Thiscorrelation may be performed by different procedures, for example byperforming a multiplication by the modulation pulse g(t) then an FFT.

The signal obtained after this correlation, denoted z_(p) in whatfollows and in the figures, may be written in the following manner:z _(p)=α_(p) ·r _(p)  (7)

where α_(p) and r_(p) are complex numbers that correspond respectivelyto the value of the fading and to the interference-affected value of theuseful symbol having degraded the symbol in the course of thetransmission through the transmission channel.

Owing to the orthogonality property of the symbols, the number r_(p) infact comprises the original useful symbol and furthermore aninterference term, which originates from interference due to thetransmission of the neighboring symbols. This interference is, byconstruction of OFDM systems of density 2, orthogonal to the originaluseful symbol.

Thus, if the symbol transmitted S_(p) was real (i.e. if c_(p) is a realnumber equal to a_(p)), we then have:r _(p) =a _(p) +i.int _(p)  (8)

where the term i.int_(p) represents the interference and is a pureimaginary number (that is to say the number int_(p) is a real number).

Conversely, if the symbol transmitted was pure imaginary (i.e. if c_(p)is a pure imaginary number, equal to i·b_(p), we then have:r _(p) =int _(p) +i.b _(p)  (9)

where the term int_(p) represents the interference and is a real number.

In a step 33, the estimation of the fading is then carried out for eachof the pilot symbols contained in the frame. That is to say theconditions of propagation through the transmission channel are estimatedfor the pilot symbols, whose location in the frame and whose value areknown to the receiver in advance.

In a step 34, one then proceeds to what is referred to as the channeltracking. For this purpose, one or more interpolations are performed, onthe basis of the estimated values obtained in step 33, so as to produceestimated values of the fading for the other symbols of the frame(symbols corresponding to useful information).

An estimated value, denoted {circumflex over (α)}_(p) in what followsand in the figures, of the fading is thus obtained for each symbol ofthe frame.

Finally, in a step 35, the symbols transmitted (in particular thesymbols other than the pilot symbols, since those are the ones thatcarry the useful information) are estimated by performing the followingcalculation for each:ĉ _(p) =z _(p)/{circumflex over (α)}_(p)  (10)

The invention relates to step 33 above, by which the fading is estimatedfor the pilot symbols of the frame. The invention relates in fact tochannel estimating methods and devices.

The diagram of FIG. 4 a illustrates the steps of a method according to afirst aspect of the invention.

In a step 91, on the one hand K values of the signal received areselected, where K is an integer greater than or equal to unity. Theexpression signal received is understood here to mean the radio signalreceived by the receiver, considered after the synchronization step 31and correlation step 32. The K values thus selected correspond to one ormore real pilot symbols S_(k). These K values are denoted z_(k), where kis an integer index lying between 1 and K (1≦k≦K) of the signalreceived. Moreover, the respective values of the real pilot symbolsS_(k) transmitted are denoted c_(k).

Moreover, L values of the signal received (in the sense indicated above)are also selected. These values are denoted z_(l), and correspondrespectively to one or more pure imaginary pilot symbols denoted S_(l),of respective values denoted c_(l), where L is an integer greater thanor equal to unity and where l is an index lying between 1 and L (1≦l≦L).

The pilot symbols S_(k) and S_(l) are not picked at random. On thecontrary, they are pilot symbols that are sufficiently close togetherboth along the frequency axis and along the time axis for it to bepossible for the fading of the signal through the transmission channelto be considered to have had a substantially identical complex value (inmodulus and in phase) for these pilot symbols. This complex value isdenoted α. Moreover, the inverse of this complex number is denoted β(that is to say β=1/α).

In a step 92, we then determine complex numbers u and v and a realnumber λ which minimize the following least squares expression:

$\begin{matrix}{ɛ_{1}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot u} )} - {\lambda \cdot c_{k}}}}^{2}} + {\sum\limits_{1}{{{{Re}( {z_{1} \cdot v} )} - {\lambda \cdot c_{1}}}}^{2}}}} & (11)\end{matrix}$

where the sign Σ denotes the summation operator,

where ∥x∥ denotes the absolute value operator for the real variable x orthe modulus of the complex variable x,

where λ is a real number,

where u and v are orthogonal (that is to say Re(u*.v)=0, where Re(x)denotes the real part operator for the complex number x, and where x*denotes the complex conjugate of the complex number x), such that∥u∥=∥v∥.

For example, it will be possible to take v=−i·u, where i denotes thesquare root of the relative integer −1, that is to say the complexnumber e^(−i·π)/2.

In a step 93, an estimated value {circumflex over (α)} of the value α ofthe fading of the signal through the transmission channel is determinedfor the pilot symbols concerned, that is to say for the pilot symbolsS_(k) and S_(l) selected in step 91, by calculating:{circumflex over (α)}=λ/u  (12)

This estimated value {circumflex over (α)} holds for the pilot symbolsS_(k) and S_(l). Of course, steps 91 to 93 are preferably repeated insuch a way as to produce estimated values & of the value α of the fadingof the signal through the transmission channel for all the pilot symbolsof the frame, or at least for all those of these pilot symbols that aretaken into account for performing the channel tracking (step 34 of FIG.3).

The least squares expression (11) above will be understood better afterthe following description of two modes of implementation of theinvention, offered below with regard to FIGS. 4 b and 4 c, of which itconstitutes a generalization.

A first mode of implementation is described below with regard to thechart of steps of FIG. 4 b.

In this mode of implementation, the method comprises a selection step41, which is identical to step 91 described above, and steps 42 and 43,which correspond to steps 92 and 93 respectively mentioned above.

Firstly, let us assume that K=L=1. Stated otherwise, let us assume that,in step 41, a single value z₁ of the signal received has been selected,corresponding to one and only one real pilot symbol S₁ of value c₁ onthe one hand, and a single value z₂ of the signal received has beenselected, corresponding to one and only one pure imaginary pilot symbolS₂ of value c₂ on the other hand.

For the symbol S₁ of value c₁ transmitted as real symbol, we may write:Re(z ₁.β)=c ₁  (13)

and, for the symbol S₂ of value c₂ transmitted as pure imaginary symbol,we can also write:Im(z ₂.β)=c ₂  (14)

where Re(x) designates the real part operator for the complex variablex, and

where Im(x) denotes the pure imaginary part operator for the complexvariable x.

We can therefore form the system of equations:

$\begin{matrix}\{ \begin{matrix}{{{{Re}( {z_{1} \cdot \beta} )} - c_{1}} = 0} \\{{{{Im}( {z_{2} \cdot \beta} )} - c_{2}} = 0}\end{matrix}  & (15)\end{matrix}$

In a calculation step 42, the above system of equations is solved toobtain Re(β) and Im(β). The complex number β=Re(β)+i·Im(β) is thusobtained, given by:

$\begin{matrix}{\beta = \frac{{c_{1} \cdot z_{2}^{*}} + {c_{2} \cdot {\mathbb{i}} \cdot z_{1}^{*}}}{{Re}( {z_{1} \cdot z_{2}^{*}} )}} & (16)\end{matrix}$

where z₁* and z₂* designate respectively the complex number defined bythe conjugate of z₁ and the complex number defined by the conjugate ofz₂.

This calculation generalizes to other cases, that is to say to the caseswhere (K,L)≠(1,1) by assigning the indices k to the pilot symbols(selected in step 41) which were transmitted as real pilot symbols, andthe indices l to the pilot symbols (selected in step 41) which weretransmitted as pure imaginary symbols.

Step 42 then consist in determining the real numbers Re(β) and Im(β)which minimize the following least squares expression:

$\begin{matrix}{ɛ_{2}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot \beta} )} - c_{k}}}^{2}} + {\sum\limits_{1}{{{{Im}( {z_{1} \cdot \beta} )} - c_{1}}}^{2}}}} & (17)\end{matrix}$

where the sign Σ denotes the summation operator,

where ∥x∥ denotes the absolute value operator for the real variable x.

The least squares expression (17) corresponds to the least squaresexpression (11) of the general case, putting λ equal to unity, u equalto β, and v equal to −i·β. Stated otherwise, the first mode ofimplementation of the method in accordance with the chart of steps ofFIG. 4 b is deduced from the general case by putting λ equal to unity, uequal to β and v equal to −i·β.

The numbers Re(β) and Im(β) sought are those which minimize thefollowing least squares expression:

${{ɛ_{2}^{2} = {{\sum\limits_{k}{{{{{{Re}( z_{k} )} \cdot {Re}}\;(\beta)} - {{{{Im}( z_{k} )} \cdot {Im}}\;(\beta)} - c_{k}}}^{2}} +}}\quad}{\quad{\underset{1}{\sum}{{{{Re}( z_{1} )} \cdot {\quad{{{Im}(\beta)} + {{{{Im}( z_{1} )} \cdot {Re}}\;(\beta)} - c_{1}}}^{2}}}}}$

In an example, step 42 may consist in solving the following system oftwo equations in two unknowns:

$\begin{matrix}\{ \begin{matrix}{\frac{\partial ɛ_{2}^{2}}{\partial{{Re}(\beta)}} = 0} \\{\frac{\partial ɛ_{2}^{2}}{\partial{{Im}(\beta)}} = 0}\end{matrix}  & (18)\end{matrix}$

It can be shown that, by solving this system of equations, we thenobtain:

$\begin{matrix}{{{Re}(\beta)} = \frac{A \times B \times C \times D}{{E \times B} - D}} & (19)\end{matrix}$

on the one hand, and

$\begin{matrix}{{{Im}(\beta)} = \frac{{C \times E} + {A \times D}}{{E \times B} - D}} & (20)\end{matrix}$

on the other hand,

${{{where}\mspace{14mu} A} = {{\sum\limits_{k}{c_{k} \cdot {{Re}( z_{k} )}}} + {\sum\limits_{1}{c_{1} \cdot {{Im}( z_{1} )}}}}};$${{{where}\mspace{14mu} B} = {{\sum\limits_{k}{{Im}( z_{k} )}^{2}} + {\sum\limits_{1}{{Re}( z_{1} )}^{2}}}};$${{{where}\mspace{14mu} C} = {{- {\sum\limits_{k}{c_{k} \cdot {{Re}( z_{k} )}}}} + {\sum\limits_{1}{c_{1} \cdot {{Im}( z_{1} )}}}}};$${{{where}\mspace{14mu} D} = {{\sum\limits_{k}{{{Re}( z_{k} )} \cdot {{Im}( z_{k} )}}} - {\sum\limits_{1}{{{Im}( z_{1} )} \cdot {{Re}( z_{1} )}}}}};\mspace{14mu}{and}$${{where}\mspace{14mu} E} = {{\sum\limits_{k}{{Re}( z_{k} )}^{2}} + {\sum\limits_{1}{{{Im}( z_{1} )}^{2}.}}}$

The method therefore makes it possible to take into account any numberof pilot symbols, and hence to introduce diversity as appropriate. Thesimplest mode of implementation, and hence the least expensive incomputation time, is however, that where only two pilot symbols alone(one of which is a real pilot symbol and one a pure imaginary pilotsymbol) are selected in step 41.

In a step 43, an estimated value {circumflex over (α)} of the value α ofthe fading of the signal through the transmission channel is finallydetermined by inverting the complex number Re(β)+i·Im(β). It can beverified that this step 43 is deduced from the definition of step 93 ofthe general case given above, with λ equal to unity, and u equal to β.

This estimated value {circumflex over (α)} holds for the pilot symbolsS_(k) and S_(l). Of course, steps 41 to 43 are preferably repeated insuch a way as to produce estimated values {circumflex over (α)} of thevalue α of the fading of the signal through the transmission channel forall the pilot symbols of the frame, or at least for all those of thesepilot symbols that are taken into account for performing the channeltracking (step 34 of FIG. 3).

In a second mode of implementation of the method, illustrated by thechart of steps of FIG. 4 c, an estimated value {circumflex over (α)} ofthe fading of the signal through the transmission channel can bedetermined directly.

This mode of implementation comprises a step 61 which is identical tothe step 91 described above, and a step 62 which is the equivalent ofstep 92 described above. Step 62 nevertheless makes it possible tocircumvent step 93, which therefore has no equivalent in this mode ofimplementation.

According to this variant in fact, step 92 is performed by putting λequal to ρ, u equal to e^(−i·φ), and v equal to −i·e^(−i·φ), where ρ andφ are real numbers that designate respectively the modulus and the phaseof {circumflex over (α)} ({circumflex over (α)}=ρ·e^(i·φ)).

Thus step 92 and step 93 are carried out jointly, in a calculation stepdenoted 62, and consist in determining an estimated value {circumflexover (α)} of the fading of the signal through the transmission channelfor the pilot symbols concerned, which value is defined by {circumflexover (α)}=ρ·e^(i·φ) where ρ and φ minimize the following least squaresexpression:

$\begin{matrix}{ɛ_{3}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{k}}}}^{2}} + {\sum\limits_{1}{{{{Im}( {z_{1} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{1}}}}^{2}}}} & (21)\end{matrix}$

where the sign Σ denotes the summation operator,

where ∥x∥ denotes the absolute value operator for the real variable x,

where Re(x) denotes the real part operator for the complex variable x,and

where Im(x) denotes the pure imaginary part operator for the complexvariable x.

Stated otherwise, in step 62 an estimated value {circumflex over (α)} ofthe fading of the signal through the transmission channel is determinedfor the pilot symbols S_(k) and S_(l) concerned, which value is definedin polar coordinates by {circumflex over (α)}=ρ·e^(i·φ), where ρ and φare real numbers, whose value is obtained by making these numbersminimize the least squares expression (21) above.

This estimated value {circumflex over (α)} holds for the pilot symbolsS_(k) and S_(l). Of course, steps 61 and 62 are repeated in such a wayas to produce estimated values {circumflex over (α)} of the value α ofthe fading of the signal through the transmission channel for all thepilot symbols of the frame, or at least for all those of these pilotsymbols that are taken into account for performing the channel tracking(step 34 of FIG. 3).

In an example, step 62 can consist in solving the following system ofequations:

$\begin{matrix}\{ \begin{matrix}{\frac{\partial ɛ_{3}^{2}}{\partial\rho} = 0} \\{\frac{\partial ɛ_{3}^{2}}{\partial\varphi} = 0}\end{matrix}  & (22)\end{matrix}$

By matrix calculation, we then obtain an expression for tan(φ) on theone hand, and for ρ in the form of a function of φ on the other hand(ρ=f(φ)).

In the simplest case where, in step 91, the value z₁ of the signalreceived is selected, corresponding to one and only one real pilotsymbol of value c₁, on the one hand, and the value z₂ of the signalreceived is selected, corresponding to one and only one pure imaginarypilot symbol of value c₂ on the other hand, step 62 comprises thesolving of the following system with two equations:

$\begin{matrix}\{ \begin{matrix}{{{{Re}( {z_{1} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{1}}} = 0} \\{{{{Im}( {z_{2} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{2}}} = 0}\end{matrix}  & (23)\end{matrix}$

The symbols selected in step 91 (in the general case with regard to FIG.4 a), in step 41 (in the first mode of implementation described abovewith regard to FIG. 4 b) or in step 61 (in the second mode ofimplementation described above with regard to FIG. 4 c), may belong toone and the same single frame. Nevertheless, they may also belong to twoframes transmitted consecutively through the transmission channel, fromthe moment that the condition of proximity both in the direction of thefrequency axis and in the direction of the time axis, which was definedabove, is complied with for these symbols.

This condition is complied with when the pilot symbols S_(k) and S_(l)belong to a block of pilot symbols within the sense defined above, suchas the blocks 51 of the exemplary frame represented in FIG. 2.

Preferably, the pilot symbols S_(k) and S_(l) thus selected belong to agroup of pilot symbols that are pairwise adjacent in the frame, in thedirection of the frequency axis and/or in the direction of the timeaxis. This is the case in particular for the pilot symbols belonging tothe blocks 51 (whose dimensions are equal to 3×2) of the exemplary framerepresented in FIG. 2.

FIG. 5 shows the diagram of a device according to the invention,appropriate for the implementation of the method described above withregard to FIGS. 4 a-4 c. The means for executing step 93 of FIG. 4 a orstep 43 of FIG. 4 b being represented by dashes in FIG. 5, insofar asthese means of the device do not exist as such in a device for theimplementation of the method according to the mode of implementation inaccordance with the diagram of FIG. 4 c.

The device described is here integrated into a radio receiver, whichcomprises an antenna 71 for receiving the radio signal transmittedthrough the transmission channel constituted by the air. The signalpicked up by the antenna 71 is amplified by a reception amplifier 72,then filtered by a bandpass filter 73 centered on the frequency band ofthe radio channel.

The signal thus amplified and filtered is then fed to the input of asynchronization module 74 carrying out the frequency and timesynchronization of the signal.

The signal output by the module 74 is transmitted to the input of asampling module 75, which receives a sampling frequency Fe delivered byan oscillator 76. This module 75 produces the aforesaid values z_(p).The latter are stored in a memory 77 of the receiver.

The device according to the invention comprises specifically a selectionmodule 78, which performs the selection step 91, 41 or 61, on the basisof the values z_(p) stored in the memory 77.

It furthermore comprises a calculation module 79, which performs thecalculation step 92, 42 or 62 on the basis of the K values z_(k) and theL values z_(l) selected by the selection module 78. This module 79delivers the complex number β in the case of the mode of implementationof the method in accordance with FIG. 4 b, or the estimated value{circumflex over (α)} in the case of the mode of implementation of themethod in accordance with FIG. 4 c.

For the implementation of the method in the general case in accordancewith FIG. 4 a, or according to the mode of implementation in accordancewith FIG. 4 b, the device furthermore comprises an inversion module 80.In the general case, the module 80 inverts the complex number u.According to the mode of implementation in accordance with FIG. 4 b, themodule 80 inverts the complex number β provided by the calculationmodule 79, so as to deliver the estimated value {circumflex over (α)}.

The modules 78, 79 and 80 access the memory 77. They may be embodied inthe form of software modules, the demodulation means of the receiverincluded.

1. A method of estimating a transmission channel on the basis of asignal received after transmission through said transmission channel,said signal being a multicarrier signal constructed on a time/frequencylattice defined by a frequency axis and a time axis, and comprisingframes having M×N symbols distributed over M subcarriers each of whichis divided into N determined symbol times, each frame comprising P pilotsymbols distributed timewise and frequencywise in such a way as to coverthe frame according to a lattice structure, where the numbers M, N and Pare nonzero integers, the pilot symbols comprising on the one handsymbols known as real pilot symbols, transmitted as symbols having areal value, and on the other hand symbols known as pure imaginary pilotsymbols, transmitted as symbols having a pure imaginary value, themethod comprising the steps of: a) selecting one or more values z_(k) ofthe signal received corresponding to one or more real pilot symbols ofrespective values c_(k) on the one hand, and one or more values z_(l) ofthe signal received corresponding respectively to one or more pureimaginary pilot symbols of respective values c_(l) on the other hand,these pilot symbols being sufficiently close together both along thefrequency axis and along the time axis for it to be possible to considerthat the fading of the signal through the transmission channel has had asubstantially identical (in modulus and in phase) complex value α forthese pilot symbols; b) determining complex numbers u and v and a realnumber λ by minimizing the following least squares expression:$ɛ_{1}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot u} )} - {\lambda \cdot c_{k}}}}^{2}} + {\sum\limits_{1}{{{{Re}( {z_{1} \cdot v} )} - {\lambda \cdot c_{1}}}}^{2}}}$where the sign Σ denotes the summation operator, where ∥x∥ denotes theabsolute value operator for the real variable x or the modulus of thecomplex variable x, where λ is a real number, where k is an integerindex between 1 and the number of values z_(k), where u and v areorthogonal (that is to say Re(u*.v)=0, where Re(w) denotes the real partoperator for the complex number w, and where w* denotes the complexconjugate of the complex number w), such that ∥u∥=∥v∥, c) determining anestimated value {circumflex over (α)} of the value α of the fading ofthe signal through the transmission channel for the pilot symbolsconcerned, by calculating: {circumflex over (α)}=λ/u.
 2. The method ofestimating a transmission channel of claim 1, wherein λ is equal tounity, u is equal to β, and v is equal to −i·β, where β denotes theinverse of α, wherein step b) consists in determining real numbers Re(β)and Im(β) by minimizing the following least squares expression:$ɛ_{2}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot \beta} )} - c_{k}}}^{2}} + {\sum\limits_{1}{{{{Im}( {z_{1} \cdot \beta} )} - c_{1}}}^{2}}}$where the sign Σ denotes the summation operator, where ∥x∥ denotes theabsolute value operator for the real variable x, where Re(x) denotes thereal part operator for the complex variable x, and where Im(x) denotesthe imaginary part operator for the complex variable x, and wherein stepc) consists in determining the estimated value {circumflex over (α)} ofthe value α of the fading of the signal through the transmission channelfor the pilot symbols concerned, by inverting the complex numberRe(β)+i·Im(β).
 3. The method of claim 2, wherein step b) comprises thesolving of the following system of two equations in two unknowns:$\quad\{ {\begin{matrix}{\frac{\partial ɛ_{2}^{2}}{\partial{{Re}(\beta)}} = 0} \\{\frac{\partial ɛ_{2}^{2}}{\partial{{Im}(\beta)}} = 0}\end{matrix}.} $
 4. The method of claim 2, wherein step a)comprises the selection of the value z₁ of the signal receivedcorresponding to one and only one real pilot symbol of value c₁ on theone hand, and of the value z₂ of the signal received corresponding toone and only one pure imaginary pilot symbol of value c₂ on the otherhand, and wherein step b) comprises the solving of the following systemof equations in two unknowns: $\{ {\begin{matrix}{{{{Re}( {z_{1} \cdot \beta} )} - c_{1}} = 0} \\{{{{Im}( {z_{2} \cdot \beta} )} - c_{2}} = 0}\end{matrix}.} $
 5. The method of claim 1, wherein λ is equal toρ, u is equal to e^(−i·φ), and v is equal to −i·e^(−i·φ), where ρ and φare real numbers that respectively denote the modulus and the phase of{circumflex over (α)} ({circumflex over (α)}=ρ·e^(i·φ), wherein step b)and step c) are carried out jointly and consist in determining anestimated value {circumflex over (α)} of the fading of the signalthrough the transmission channel for the pilot symbols concerned, whichvalue is defined by {circumflex over (α)}=ρ·e^(i·φ) where ρ and φminimize the following least squares expression:$ɛ_{3}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{k}}}}^{2}} + {\sum\limits_{1}{{{{Im}( {z_{1} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{1}}}}^{2}}}$where the sign Σ denotes the summation operator, where ∥x∥ denotes theabsolute value operator for the real variable x, where Re(x) denotes thereal part operator for the complex variable x, and where Im(x) denotesthe pure imaginary part operator for the complex variable x.
 6. Themethod of claim 5, wherein step b) comprises the solving of thefollowing system of two equations in two unknowns:$\quad\{ {\begin{matrix}{\frac{\partial ɛ_{3}^{2}}{\partial\rho} = 0} \\{\frac{\partial ɛ_{3}^{2}}{\partial\varphi} = 0}\end{matrix}.} $
 7. The method of claim 5, wherein step a)comprises the selection of the value z₁ of the signal receivedcorresponding to one and only one real pilot symbol of value c₁ on theone hand, and of the value z₂ of the signal received corresponding toone and only one pure imaginary pilot symbol of value c₂ on the otherhand, and wherein step b) comprises the solving of the following systemof equations in two unknowns: $\{ {\begin{matrix}{{{{Re}( {z_{1} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{1}}} = 0} \\{{{{Im}( {z_{2} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{2}}} = 0}\end{matrix}.} $
 8. The method of claim 1, wherein the symbolsselected in step a) belong to one and the same single frame.
 9. Themethod of claim 1, wherein the symbols selected in step a) belong to twoframes transmitted consecutively through the transmission channel. 10.The method of claim 1, wherein the symbols selected in step a) belong toa group of pilot symbols that are pairwise adjacent in the frame, in thedirection of the frequency axis and/or in the direction of the timeaxis.
 11. A device for estimating a transmission channel on the basis ofa signal received after transmission through said transmission channel,said signal being a multicarrier signal constructed on a time/frequencylattice defined by a frequency axis and a time axis, and comprisingframes having M×N symbols distributed over M subcarriers each of whichis divided into N determined symbol times, each frame comprising P pilotsymbols distributed timewise and frequencywise in such a way as to coverthe frame according to a lattice structure, where the numbers M, N and Pare nonzero integers, the pilot symbols comprising on the one handsymbols known as real pilot symbols, transmitted as symbols having areal value, and on the other hand symbols known as pure imaginary pilotsymbols, transmitted as symbols having a pure imaginary value,comprising: means for selecting one or more values z_(k) of the signalreceived corresponding to one or more real pilot symbols of respectivevalues c_(k) on the one hand, and one or more values z_(l) of the signalreceived corresponding respectively to one or more pure imaginary pilotsymbols of respective values c_(l) on the other hand, these pilotsymbols being sufficiently close together both along the frequency axisand along the time axis for it to be possible to consider that thefading of the signal through the transmission channel has had asubstantially identical complex value α for these pilot symbols; meansfor determining complex numbers u and v and a real number x minimizingthe following least squares expression:$ɛ_{1}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot u} )} - {\lambda \cdot c_{k}}}}^{2}} + {\sum\limits_{1}{{{{Re}( {z_{1} \cdot v} )} - {\lambda \cdot c_{1}}}}^{2}}}$where the sign Σ denotes the summation operator, where ∥x∥ denotes theabsolute value operator for the real variable x or the modulus of thecomplex variable x, where λ is a real number, where k is an integerindex between 1 and the number of values z_(k), where u and v areorthogonal (that is to say Re(u*.v)=0, where Re(w) denotes the real partoperator for the complex number w, and where w* denotes the complexconjugate of the complex number w), such that ∥u∥=∥v∥, means fordetermining an estimated value {circumflex over (α)} of the value α ofthe fading of the signal through the transmission channel for the pilotsymbols concerned, by calculating: {circumflex over (α)}=λ/u.
 12. Adevice for estimating a transmission channel on the basis of a signalreceived after transmission through said transmission channel, saidsignal being a multicarrier signal constructed on a time/frequencylattice defined by a frequency axis and a time axis, and comprisingframes having M×N symbols distributed over M subcarriers each of whichis divided into N determined symbol times, each frame comprising P pilotsymbols distributed timewise and frequencywise in such a way as to coverthe frame according to a lattice structure, where the numbers M, N and Pare nonzero integers, the pilot symbols comprising on the one handsymbols known as real pilot symbols, transmitted as symbols having areal value, and on the other hand symbols known as pure imaginary pilotsymbols, transmitted as symbols having a pure imaginary value,comprising: means for selecting one or more values z_(k) of the signalreceived corresponding to one or more real pilot symbols of respectivevalues c_(k) on the one hand, and one or more values z_(l) of the signalreceived corresponding respectively to one or more pure imaginary pilotsymbols of respective values c_(l) on the other hand, these pilotsymbols being sufficiently close together both along the frequency axisand along the time axis for it to be possible to consider that thefading of the signal through the transmission channel has had asubstantially identical complex value α for these pilot symbols; meansfor determining real numbers Re(β) and Im(β) minimizing the followingleast squares expression:$ɛ_{2}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot \beta} )} - c_{k}}}^{2}} + {\sum\limits_{1}{{{{Im}( {z_{1} \cdot \beta} )} - c_{1}}}^{2}}}$where the sign Σ denotes the summation operator, where ∥x∥ denotes theabsolute value operator for the real variable x, where k is an integerindex between 1 and the number of values z_(k), where Re(x) denotes thereal part operator for the complex variable x, where Im(x) denotes thepure imaginary part operator for the complex variable x, and where βdenotes the inverse of α; and, means for determining an estimated value{circumflex over (α)} of the fading of the signal through thetransmission channel for the pilot symbols concerned, by inverting thecomplex number Re(β)+i·Im(β).
 13. A device for estimating a transmissionchannel on the basis of a signal received after transmission throughsaid transmission channel, said signal being a multicarrier signalconstructed on a time/frequency lattice defined by a frequency axis anda time axis, and comprising frames having M×N symbols distributed over Msubcarriers each of which is divided into N determined symbol times,each frame comprising P pilot symbols distributed timewise andfrequencywise in such a way as to cover the frame according to a latticestructure, where the numbers M, N and P are nonzero integers, the pilotsymbols comprising on the one hand symbols known as real pilot symbols,transmitted as symbols having a real value, and on the other handsymbols known as pure imaginary pilot symbols, transmitted as symbolshaving a pure imaginary value, comprising: means for selecting one ormore values z_(k) of the signal received corresponding to one or morereal pilot symbols of respective values c_(k) on the one hand, and oneor more values z_(l) of the signal received corresponding respectivelyto one or more pure imaginary pilot symbols of respective values c_(l)on the other hand, these pilot symbols being sufficiently close togetherboth along the frequency axis and along the time axis for it to bepossible to consider that the fading of the signal through thetransmission channel has had a substantially identical complex value αfor these pilot symbols; and means for determining an estimated value{circumflex over (α)} of the fading of the signal through thetransmission channel for the pilot symbols concerned, which value isdefined by {circumflex over (α)}=ρ·e^(i·φ) where ρ and φ are realnumbers which minimize the following least squares expression:$ɛ_{3}^{2} = {{\sum\limits_{k}{{{{Re}( {z_{k} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{k}}}}^{2}} + {\sum\limits_{1}{{{{Im}( {z_{1} \cdot {\mathbb{e}}^{{- {\mathbb{i}}} \cdot \varphi}} )} - {\rho \cdot c_{1}}}}^{2}}}$where the sign Σ denotes the summation operator, where ∥x∥ denotes theabsolute value operator for the real variable x, where k is an integerindex between 1 and the number of values z_(k), here Re(x) denotes thereal part operator for the complex variable x, and where Im(x) denotesthe pure imaginary part operator for the complex variable x.